In the previous section,
we used all random variables to estimate \(\mu \) . However, due to CIs encoded by the graph structure in a Bayesian network \(\mathcal {B}\) , observed states and CPDs of only some variables “might” be required for computing \(\mu \) . These variables are called requisite variables. To get a better estimate of \(\mu \) , it is recommended to use only these variables. The standard approach is to first apply the Bayes-ball algorithm [1]} over the graph to obtain a sub-network of requisite variables, then simulate the sub-network to obtain the weighted samples. An alternative approach is to use Bayes-ball to simulate the original network \(\mathcal {B}\)  and focus on only requisite variables to obtain the weighted samples. This approach is trivial and might already be used by many BN inference tools. However, it is not described in the literature clearly, so we will describe it next. It will form the basis of our discussion on CS-LW, where we will also exploit structures within CPDs of BNs.
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